docs: def det_4x3(a,b,c,d):
      '''
      det_4x3(a,b,c,d) yields the determinate of the matrix formed the given rows, which may have
        more than 1 dimension, in which case the later dimensions are multiplied and added point-wise.
        The point's must be 3D points; the matrix is given a fourth column of 1s and the resulting
        determinant is of this matrix. 
      '''
      # I just solved this in Mathematica, copy-pasted, and replaced the string '] m' with ']*m':
      # Mathematica code: Det@Table[If[j == 3, 1, i[j]], {i, {a, b, c, d}}, {j, 0, 3}]
      return (a[1]*b[2]*c[0] + a[2]*b[0]*c[1] - a[2]*b[1]*c[0] - a[0]*b[2]*c[1] -
              a[1]*b[0]*c[2] + a[0]*b[1]*c[2] + a[2]*b[1]*d[0] - a[1]*b[2]*d[0] -
              a[2]*c[1]*d[0] + b[2]*c[1]*d[0] + a[1]*c[2]*d[0] - b[1]*c[2]*d[0] -
              a[2]*b[0]*d[1] + a[0]*b[2]*d[1] + a[2]*c[0]*d[1] - b[2]*c[0]*d[1] -
              a[0]*c[2]*d[1] + b[0]*c[2]*d[1] + a[1]*b[0]*d[2] - a[0]*b[1]*d[2] -
              a[1]*c[0]*d[2] + b[1]*c[0]*d[2] + a[0]*c[1]*d[2] - b[0]*c[1]*d[2])